Szwarc constant

Electrochemical considerations. There is so much evidence from electrical and also from non-electrical studies for the existence of ion-pairs in solvents of low polarity, that it cannot be ignored in discussing the reactions of ions in such systems [136]. The most detailed and comprehensive discussion of ion-pairs and related concepts has been given by Szwarc [137]. The next step after the recognition of the existence of ion-pairs is the estimation of their concentration as a function of the various experimental parameters, so that their importance relative to the free ions can be assessed. In order to do this, the dissociation constant of the ion-pairs under the relevant conditions is required. 

This is not the first time that the kinetics of bulk polymerizations has been analysed critically. Szwarc (1978) has made the same objection to the identification of the rate constant for the chemically initiated bulk polymerization of tetrahydrofuran as a second-order rate constant, k, and he related the correct, unimolecular, rate constant to the reported by an equation identical to (3.2). Strangely, this fundamental revaluation of kinetic data was dismissed in three lines in a major review (Penczek et al. 1980). Evidently, it is likely to be relevant to all rate constants for cationic bulk polymerizations, e.g., those of trioxan, lactams, epoxides, etc. Because of its general importance I will refer to this insight as Szwarc s correction and to (3.2) as Szwarc s equation . 

In Table 2 we present the new unimolecular propagation rate-constants k+Bpl for bulk polymerizations, calculated from the published bimolecular pl by Szwarc s... 

Szwarc and coworkers have reported equilibrium constants for the disproportionation reaction given in equation 40 ... 

The hydroxide ion is usually not sufficiently nucleophilic to reinitiate polymerization and the kinetic chain is broken. Water has an especially negative effect on polymerization, since it is an active chain-transfer agent. For example, C s is approximately 10 in the polymerization of styrene at 25°C with sodium naphthalene [Szwarc, 1960], and the presence of even small concentrations of water can greatly limit the polymer molecular weight and polymerization rate. The adventitious presence of other proton donors may not be as much of a problem. Ethanol has a transfer constant of about 10-3. Its presence in small amounts would not prevent the formation of high polymer because transfer would be slow, although the polymer would not be living. 

Let us assume that fci is equal to k9, the rate constant for the gas phase decomposition (15), where no cage effect is expected. This assumption does not always hold (15, 18). For example, it is known (18) that di-f erf-butyl peroxide (DPB) decomposes about 30% slower in the gas phase than in solution. We can calculate from our value of k8 and the known value of kg, from the work of Szwarc (7, 21), a value for the fraction of acetoxy radical pairs recombining, fR, where... 

Bhattacharyya, D. N., C. L. Lee, J. Smid, and M. Szwarc The absolute rate constants of anionic propagation by free ions and ion pairs of living polystyrene. Polymer 5, 54 (1964). 

Fig. 2. Equilibrium constant for polymerization of a-methylstyrene to living oligomers and to a high molecular weight polymer. (O) Vrancken, SmiD, and Szwarc ( ) Worsfold and Bywater (A) McCormick. Reproduced, with permission, from Vrancken, Smid, and Szwarc Trans. Faraday Soc. 58, 2036 (1962).

A different and independent approach to determine the parameters of KC8 is made by conductivity measurements. The dissociation constant of carbanionic compounds displays no simple temperature dependence according to the van t Hoff equation as Worsfold and Bywater (32) and Szwarc (33) have already shown. When we assume two types of ion pairs, the experimentally measured dissociation constant is given by... 

Szwarc and Wang161) have claimed, without citing any supportive experimental measurements, that the equilibrium constant for the process shown in Eq. (11) is approximately one a value in stark contrast to that of ca. 160 LM-1 reported by Morton.42) Their assessment is not supported by the viscometric measurements,42) the kinetic findings of Bywater and Worsfold,156) the association measurements reported by West and Waack56) (Table 3) for benzyllithium in tetrahydrofuran, nor by the findings of Kminek, Kaspar, and Trekoval161a). 

Special Case where K2 = 0, q = 0, and q2 = 0. Equilibrium Constant K Depends on the Chain Length. According to Szwarc and coworkers (12, 26) the equilibrium constants of the anionic polymerization of a-methylstyrene depend on the degree of polymerization (chain lengths). For the reaction... 

With these catalysts, the cation complexes with the monomer so weakly that a solid surface and low polymerization temperatures are required to achieve sufficient orientation for stereospecificity. Braun, Herner and Kern (217) have shown that lower polymerization temperatures are required (in n-hexane diluent) to obtain isotactic polystyrene as the alkyl metal becomes more electropositive (RNa, —20° C. RK, —60° to —70° C. and RRb, —80° C.). They correlate isotacticity with the polymerization rate as a function of catalyst, temperature or solvent. However, with Alfin catalysts, stereospecific polymerization of styrene is unrelated to rate (226). A helical polymerization mechanism as proposed by Ham (229) and Szwarc (230) is also inadequate for explaining the temperature effects since the probability for adventitious formation of several successive isotactic placements should have been the same at constant temperature in the same solvent for all catalysts. 

Szwarc and co-workers [114] measured the apparent rate constant of the addition of some substituted styrenes to polystyrylsodium... 

KdisR. Ac+ are the dissociation constants of the ion pairs Rf Ac+ and R Ac+. Under suitable conditions, the equilibria (29)—(31) can be followed by spectro-photometric methods [167c, 169], There exist some very important specific reactions of the type shown in eqns. (29) and (30) which are poorly characterized. This concerns, for example, the electron transfer from naphthalene- metal+ (Szwarc initiator) to styrene or other monomers [see Chap. 3, eqn. (46)]. The rapid consecutive reactions of the styrene radical ion make a direct measurement of the equilibrium impossible. Indirect data are not reliable. 

The approaches of Gloss, Kaptein-Oosterhoff, and Adrian are based on quantitative treatments of the microscopic behaviour of radical pain. Very siiAilar results can also be obtained from a simple kinetic model which involves formal rate constants for the processes of pair reaction from singlet states k, pair escape k, and singlet-triplet transitions kf . Replacement of the actual pair behaviour by a simple kinetic scheme may be an oversimplification, thou it seems justified by the results of Szwarc and co-workers who showed that pair reaction and escape may be described to a good approximation in terms of simple first-order processes. 

M. Szwarc, Chem. Revs., 47, 75 (1950), has written an excellent review summarizing the difficulties involved in calculating individual rate constants from kinetic data for systems of consecutive reactions. 

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